Unbalanced OT often improves over the results obtained using balanced OT in most of its application to data sciences.
All these examples are also instructive to understand how the parameter \(\rho \)  should be tuned to reach good performances on large scale datasets. 
An example in image processing is for video registration using the UOT plan [1]}.
In shape registration for medical imaging [2]}, biology [3]}, [4]} and in LiDAR imaging [5]}, [6]}, UOT is used to provide assignments robust to acquisition noise.
UOT can also be used for the theoretical analysis of some statistical and machine learning methods.
It is possible to express the gradient descent training of the neurons of a two layers perceptron as a UOT gradient flow, and prove its convergence to global optimality [7]}, [8]}.
One can also state stability guarantees on the reconstruction of sparse measures in super-resolution problems using UOT [9]}.
